FoeHammer isn't necessarily very high up on the military chain of command, and the UNSC might prefer a "need-to-know" basis of disseminating information. Maybe Cortana simply omitted their involvement in the destruction because all FoeHammer needs to know is to get her butt down their and pick them up. This is the military, after all.

Wait.... wait... I had something else.... dang, I need to get to bed...

Ah, there we go.

I'm tired, and I have the vague feeling that this has been mentioned before, but...

What if, prior to this line...

"Negative, negative! We have a wildcat destabilization of the ship's fusion core. The engines must have sustained more damage than we thought! (off radio) Analyzing! We have six minutes before the fusion drives detonate. We need to evac NOW!"

... Cortana did inform FoeHammer that they were blowing up the fusion core? Remember, when you sink the final rocket/grenade, Cortana estimates fifteen minutes are left. I'm pretty sure it doesn't take most of us 9 minutes to reach the Warthog bay. In this case, the "more damage than we thought" would simply explain why you only had 6 minutes of the earlier 15 left.

As for informing FoeHammer... this is a bit of a stretch, but maybe she did it via the radio and simply didn't let you hear it. Remember, you're in a very tense situation, with Flood and Sentinels streaming at you from all directions while you're forced to aim at the fusion core instead of them. Cortana might have thought you didn't need the distraction.